That new branch looks like it's taking a lot of energy from the rest of the tree. I'd saw it off close to the base and seal the stump. If new sprouts form around the cut base of the branch's stump, snip them off right away.

Thanks everyone. The big sprout is gone. I managed to prune a lot of other dead branches out too. Glad to get this taken care of before the foliage comes out. Wonder what kind of tree it is. that's my next quest.